Press n or j to go to the next uncovered block, b, p or k for the previous block.
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527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 | import type { NumberLineState } from '../types' import { numberToScreenX } from '../numberLineTicks' import { primeColorRgba } from './primeColors' import { smallestPrimeFactor } from './sieve' import { decayingSin } from '../../shared/animationMath' // --- Sieve phase timing --- export interface SievePhase { factor: number startMs: number durationMs: number } export const SIEVE_PHASES: SievePhase[] = [ { factor: 2, startMs: 4000, durationMs: 5000 }, // seg 1: sweep 4000–9000, tail 9000–10200 { factor: 3, startMs: 10200, durationMs: 3000 }, // seg 2: sweep 10200–13200, tail 13200–14400 { factor: 5, startMs: 14400, durationMs: 1800 }, // seg 3a: sweep 14400–16200 { factor: 7, startMs: 16600, durationMs: 1300 }, // seg 3b: sweep 16600–17900 { factor: 11, startMs: 18300, durationMs: 800 }, // seg 3c: sweep 18300–19100, tail 19100–20300 ] export const CELEBRATION_START_MS = 20300 export const COMPOSITION_START_MS = CELEBRATION_START_MS + 5000 // 25300 — after celebration settles /** The composite number used for the factorization reveal */ const COMPOSITION_EXAMPLE = 12 /** How long each factor's arc chain takes to draw (ms per arc) */ const COMPOSITION_ARC_STAGGER_MS = 300 /** * Fixed maximum N for sweep calculations. All sweep progress, composite mark * timing, and hopper position use this constant so they stay in sync with the * viewport tracking in getSieveViewportState. Viewport-dependent bounds are * only used for visibility culling (deciding which composites to draw). */ export const SWEEP_MAX_N = 130 // --- Per-composite animation --- /** Timing constants for each composite's animation after being marked */ const FLASH_DURATION = 120 const SHAKE_DURATION = 130 // 120–250ms after mark const FALL_DURATION = 350 // 250–600ms after mark const ANIM_TOTAL = FLASH_DURATION + SHAKE_DURATION + FALL_DURATION // 600ms interface CompositeAnimState { factor: number // which prime factor marked it markTimeMs: number // exact dwellElapsedMs when sweep reached it } // --- Easing helpers --- function clamp01(x: number): number { return Math.max(0, Math.min(1, x)) } function easeInQuad(t: number): number { return t * t } function easeOutQuint(t: number): number { return 1 - (1 - t) ** 5 } /** Per-factor sweep easing: slow start → fast finish */ function sweepEase(t: number, factor: number): number { // Factors 2, 3: ease-in quad (t²) — 50% of time covers first 25% of range // Factors 5, 7: gentler t^1.5 — fewer composites to show const power = factor <= 3 ? 2 : 1.5 return t ** power } function easeOutCubic(t: number): number { return 1 - (1 - t) ** 3 } /** Decompose n into its prime factors, e.g. 12 → [2, 2, 3] */ function primeFactors(n: number): number[] { const factors: number[] = [] let remaining = n while (remaining > 1) { const p = smallestPrimeFactor(remaining) if (p <= 1) break factors.push(p) remaining /= p } return factors } /** * Group prime factors into skip-counting chains for the composition reveal. * e.g. 12 → [{ factor: 2, multiples: [2, 4, 6, 8, 10, 12] }, { factor: 3, multiples: [3, 6, 9, 12] }] * Each chain shows the full skip-counting path from the factor up to N. */ function compositionChains(n: number): { factor: number; multiples: number[] }[] { const factors = primeFactors(n) const seen = new Set<number>() const chains: { factor: number; multiples: number[] }[] = [] for (const f of factors) { if (seen.has(f)) continue seen.add(f) const multiples: number[] = [] for (let m = f; m <= n; m += f) { multiples.push(m) } chains.push({ factor: f, multiples }) } return chains } // --- Sieve debug tuning (module-level, same pattern as goldenRatioDemo) --- let sieveTrackingRange = 20 let sieveFollowHops = 15 export function getSieveTrackingRange(): number { return sieveTrackingRange } export function setSieveTrackingRange(v: number): void { sieveTrackingRange = Math.max(5, v) } export function getSieveFollowHops(): number { return sieveFollowHops } export function setSieveFollowHops(v: number): void { sieveFollowHops = Math.max(1, Math.round(v)) } // --- Compute marked composites with exact mark times --- function computeCompositeStates( maxN: number, dwellElapsedMs: number, viewportRight?: number ): Map<number, CompositeAnimState> { const composites = new Map<number, CompositeAnimState>() for (const phase of SIEVE_PHASES) { if (dwellElapsedMs < phase.startMs) break const p = phase.factor // Sweep starts from the factor itself (skip counting: 2, 4, 6, 8...) // but only marks composites at p*2 and beyond (p itself is prime). const sweepStart = p const firstMultiple = p * 2 const sweepRange = maxN - sweepStart if (sweepRange <= 0) continue const linearProgress = clamp01((dwellElapsedMs - phase.startMs) / phase.durationMs) const phaseProgress = sweepEase(linearProgress, p) const maxReached = sweepStart + sweepRange * phaseProgress for (let m = firstMultiple; m <= Math.min(maxN, maxReached); m += p) { if (composites.has(m)) continue // already marked by earlier factor // Compute exact time this composite was reached by the sweep // Invert the easing: find the linear t such that sweepEase(t) = fraction const fractionAlongSweep = (m - sweepStart) / sweepRange // Invert power easing: t = fraction^(1/power) const power = p <= 3 ? 2 : 1.5 const linearFraction = fractionAlongSweep ** (1 / power) const markTimeMs = phase.startMs + linearFraction * phase.durationMs composites.set(m, { factor: p, markTimeMs }) } // Once the hopper has left the viewport, mark ALL remaining multiples // of this factor as already fallen. This prevents un-eliminated composites // from being visible when the viewport zooms out. if (viewportRight !== undefined && maxReached > viewportRight) { for (let m = firstMultiple; m <= maxN; m += p) { if (composites.has(m)) continue composites.set(m, { factor: p, markTimeMs: dwellElapsedMs - ANIM_TOTAL - 1 }) } } } return composites } // --- Get active sweep info --- function getActiveSweep( dwellElapsedMs: number, maxN: number ): { factor: number; sweepX: number } | null { for (let i = SIEVE_PHASES.length - 1; i >= 0; i--) { const phase = SIEVE_PHASES[i] if (dwellElapsedMs < phase.startMs) continue const linearProgress = clamp01((dwellElapsedMs - phase.startMs) / phase.durationMs) if (linearProgress >= 1) continue const progress = sweepEase(linearProgress, phase.factor) const sweepStart = phase.factor const sweepValue = sweepStart + (maxN - sweepStart) * progress return { factor: phase.factor, sweepX: sweepValue } } return null } // --- Viewport keyframes for dynamic zoom/pan --- export interface SieveViewport { center: number pixelsPerUnit: number } export interface SievePhaseViewports { factor: number start: SieveViewport // zoomed-in: first ~10 new composites visible end: SieveViewport // zoomed-out: ~40 new composites visible } /** * Pre-compute per-factor viewport keyframes based on the distribution of * newly eliminated composites. For each factor: * - `start`: zoomed in so the first ~10 new composites fill the screen * - `end`: zoomed out so ~40 new composites are visible */ export function computeSieveViewports(cssWidth: number, maxN: number): SievePhaseViewports[] { // Run the actual sieve to find which composites are NEW for each factor const alreadyMarked = new Set<number>() const result: SievePhaseViewports[] = [] for (const phase of SIEVE_PHASES) { const p = phase.factor const newComposites: number[] = [] for (let m = p * 2; m <= maxN; m += p) { if (!alreadyMarked.has(m)) { newComposites.push(m) alreadyMarked.add(m) } } if (newComposites.length === 0) { // Fallback: shouldn't happen for factors 2,3,5,7 with maxN=120 result.push({ factor: p, start: { center: p * 5, pixelsPerUnit: cssWidth / (p * 10 * 1.4) }, end: { center: 55, pixelsPerUnit: 5 }, }) continue } // 10th new composite → zoomed-in range const nthZoomedIn = Math.min(10, newComposites.length) - 1 const zoomedInLast = newComposites[nthZoomedIn] const zoomedInRange = zoomedInLast - p const zoomedInCenter = p + zoomedInRange / 2 const zoomedInPpu = cssWidth / (zoomedInRange * 1.4) // 40th new composite (or last) → zoomed-out range const nthZoomedOut = Math.min(40, newComposites.length) - 1 const zoomedOutLast = newComposites[nthZoomedOut] const zoomedOutRange = zoomedOutLast - p const zoomedOutCenter = p + zoomedOutRange / 2 const zoomedOutPpu = cssWidth / (zoomedOutRange * 1.4) result.push({ factor: p, start: { center: zoomedInCenter, pixelsPerUnit: zoomedInPpu }, end: { center: zoomedOutCenter, pixelsPerUnit: zoomedOutPpu }, }) } return result } /** Logarithmic interpolation for smooth zoom transitions */ function lerpLog(a: number, b: number, t: number): number { const logA = Math.log(a) const logB = Math.log(b) return Math.exp(logA + (logB - logA) * t) } /** Linear interpolation */ function lerp(a: number, b: number, t: number): number { return a + (b - a) * t } /** Interpolate between two viewports using linear center + logarithmic ppu */ function lerpViewport(a: SieveViewport, b: SieveViewport, t: number): SieveViewport { return { center: lerp(a.center, b.center, t), pixelsPerUnit: lerpLog(a.pixelsPerUnit, b.pixelsPerUnit, t), } } /** * Clamp a sieve viewport so the visible range stays within bounds. * Left edge gets a 10% margin so the origin isn't flush with the screen edge. * Right edge stays at SWEEP_MAX_N to avoid showing un-sieved composites. */ function clampSieveViewport(vp: SieveViewport, cssWidth: number): SieveViewport { const halfRange = cssWidth / (2 * vp.pixelsPerUnit) let { center, pixelsPerUnit } = vp // 10% of visible width as left margin (origin isn't pinned to screen edge) const leftMargin = halfRange * 0.2 // 10% of full width = 20% of halfRange // If the viewport is wider than the usable range, zoom in to fit const usableRange = SWEEP_MAX_N + leftMargin if (2 * halfRange > usableRange) { pixelsPerUnit = cssWidth / usableRange const newHalf = cssWidth / (2 * pixelsPerUnit) center = -leftMargin + newHalf return { center, pixelsPerUnit } } // Shift center so edges don't exceed boundaries if (center + halfRange > SWEEP_MAX_N) center = SWEEP_MAX_N - halfRange if (center - halfRange < -leftMargin) center = -leftMargin + halfRange return { center, pixelsPerUnit } } /** * Map virtual dwell time → interpolated viewport for the sieve animation. * * During each sweep phase: interpolate start → end using eased progress * (same easing as the sweep itself, so slow sweep = zoomed in). * During gaps/tails between phases: quick zoom-in to next start. * During celebration: zoom out to wide view. * * All returned viewports are clamped so the visible range stays within * [0, SWEEP_MAX_N], preventing un-sieved composites from appearing. */ export function getSieveViewportState( virtualDwellMs: number, keyframes: SievePhaseViewports[], celebrationVp: SieveViewport, cssWidth = 800, maxN = 120 ): SieveViewport | null { if (keyframes.length === 0) return null // --- Factor 2 hopper-tracking --- // Follow the hopper closely for the first N hops, showing M integers // around it so kids can see skip counting clearly. Tunable via debug panel. const followUntilValue = 2 + sieveFollowHops * 2 const trackingPpu = cssWidth / (sieveTrackingRange * 1.4) // Before first phase: hold at factor 2's tracking start (centered on 2) const firstPhase = SIEVE_PHASES[0] if (virtualDwellMs < firstPhase.startMs) { return clampSieveViewport({ center: firstPhase.factor, pixelsPerUnit: trackingPpu }, cssWidth) } // During celebration → composition: multi-phase viewport transition const lastPhase = SIEVE_PHASES[SIEVE_PHASES.length - 1] const lastPhaseEnd = lastPhase.startMs + lastPhase.durationMs if (virtualDwellMs >= CELEBRATION_START_MS) { const celebDuration = 1500 const lastKf = keyframes[keyframes.length - 1] // Composition reveal: zoom into the example number if (virtualDwellMs >= COMPOSITION_START_MS) { const compVp: SieveViewport = { center: 7, pixelsPerUnit: cssWidth / (16 * 1.4) } const compTransitionMs = 1500 const compT = clamp01((virtualDwellMs - COMPOSITION_START_MS) / compTransitionMs) const eased = easeOutCubic(compT) return clampSieveViewport(lerpViewport(celebrationVp, compVp, eased), cssWidth) } // Celebration zoom const celebT = clamp01((virtualDwellMs - CELEBRATION_START_MS) / celebDuration) const eased = easeOutCubic(celebT) return clampSieveViewport(lerpViewport(lastKf.end, celebrationVp, eased), cssWidth) } // Find which phase or gap we're in for (let i = 0; i < SIEVE_PHASES.length; i++) { const phase = SIEVE_PHASES[i] const kf = keyframes[i] const phaseEnd = phase.startMs + phase.durationMs // During this sweep phase if (virtualDwellMs >= phase.startMs && virtualDwellMs < phaseEnd) { const linearT = clamp01((virtualDwellMs - phase.startMs) / phase.durationMs) const easedT = sweepEase(linearT, phase.factor) // Factor 2: track the hopper for the first 15 hops if (phase.factor === 2) { const sweepValue = phase.factor + (maxN - phase.factor) * easedT const followEndEasedT = (followUntilValue - phase.factor) / (maxN - phase.factor) if (easedT <= followEndEasedT) { // Pure tracking: center on hopper, tight zoom return clampSieveViewport({ center: sweepValue, pixelsPerUnit: trackingPpu }, cssWidth) } // Transition from tracking to regular keyframe viewport const transitionRange = 0.15 const transitionT = clamp01((easedT - followEndEasedT) / transitionRange) const eased = easeOutCubic(transitionT) const trackVp: SieveViewport = { center: sweepValue, pixelsPerUnit: trackingPpu } const regularVp = lerpViewport(kf.start, kf.end, easedT) return clampSieveViewport(lerpViewport(trackVp, regularVp, eased), cssWidth) } return clampSieveViewport(lerpViewport(kf.start, kf.end, easedT), cssWidth) } // In a gap/tail after this phase but before the next const nextPhase = SIEVE_PHASES[i + 1] if (nextPhase && virtualDwellMs >= phaseEnd && virtualDwellMs < nextPhase.startMs) { const gapDuration = nextPhase.startMs - phaseEnd const gapT = clamp01((virtualDwellMs - phaseEnd) / gapDuration) const eased = easeOutCubic(gapT) const nextKf = keyframes[i + 1] // By end of any phase (including factor 2's tracking), the viewport // has fully blended to kf.end, so the gap transition is uniform. return clampSieveViewport(lerpViewport(kf.end, nextKf.start, eased), cssWidth) } } // After last phase but before celebration: hold at last end, zoom toward celebration if (virtualDwellMs >= lastPhaseEnd && virtualDwellMs < CELEBRATION_START_MS) { const tailDuration = CELEBRATION_START_MS - lastPhaseEnd const tailT = clamp01((virtualDwellMs - lastPhaseEnd) / tailDuration) const eased = easeOutCubic(tailT) const lastKf = keyframes[keyframes.length - 1] return clampSieveViewport(lerpViewport(lastKf.end, celebrationVp, eased), cssWidth) } return null } // --- Per-tick transforms for main renderer --- export interface SieveTickTransform { opacity: number // 0 = hidden, 1 = normal offsetX: number // horizontal shake (px) offsetY: number // vertical fall (px) rotation: number // radians } /** * Compute per-tick transforms for the main renderer during the sieve animation. * Composites shake and fall off; primes are unaffected (not in the map). * * Animation is POSITION-BASED, not timestamp-based: progress is derived * directly from how far the hopper has traveled past each composite * (`hopsPast = (sweepValue - m) / factor`). This guarantees zero latency * between the hopper landing on a number and its shake/fall starting, * because they share the exact same sweepValue. */ export function computeSieveTickTransforms( maxN: number, dwellElapsedMs: number, cssHeight: number, viewportRight?: number ): Map<number, SieveTickTransform> { const transforms = new Map<number, SieveTickTransform>() const alreadyMarked = new Set<number>() // Animation thresholds in "hops past" units const SHAKE_HOPS = 0.3 const FALL_HOPS = 0.7 const TOTAL_HOPS = SHAKE_HOPS + FALL_HOPS // 1.0 hop to fully disappear for (const phase of SIEVE_PHASES) { if (dwellElapsedMs < phase.startMs) break const p = phase.factor const firstMultiple = p * 2 const sweepStart = p const sweepRange = SWEEP_MAX_N - sweepStart if (sweepRange <= 0) continue const linearProgress = clamp01((dwellElapsedMs - phase.startMs) / phase.durationMs) const sweepValue = sweepStart + sweepRange * sweepEase(linearProgress, p) // Once hopper leaves viewport, all remaining multiples are instantly gone const hopperOffScreen = viewportRight !== undefined && sweepValue > viewportRight for (let m = firstMultiple; m <= maxN; m += p) { if (alreadyMarked.has(m)) continue // Hopper hasn't reached this composite yet if (!hopperOffScreen && sweepValue < m) break // multiples are ascending alreadyMarked.add(m) // Off-screen bulk elimination: instantly hidden if (hopperOffScreen && sweepValue < m) { transforms.set(m, { opacity: 0, offsetX: 0, offsetY: 0, rotation: 0 }) continue } // How many hops past this composite the hopper has traveled const hopsPast = (sweepValue - m) / p let opacity = 1 let offsetX = 0 let offsetY = 0 let rotation = 0 if (hopsPast <= SHAKE_HOPS) { // Shake: starts the instant the hopper lands const shakeT = hopsPast / SHAKE_HOPS offsetX = decayingSin(shakeT, 4, 2) * 3 } else if (hopsPast <= TOTAL_HOPS) { // Fall: gravity drop const fallT = (hopsPast - SHAKE_HOPS) / FALL_HOPS const easedFall = easeInQuad(fallT) const driftDirection = m % 2 === 0 ? 1 : -1 offsetX = driftDirection * easedFall * 8 offsetY = easedFall * (cssHeight * 0.8) rotation = driftDirection * easedFall * 0.6 opacity = 0.6 * (1 - fallT) } else { // Fully hidden opacity = 0 } transforms.set(m, { opacity, offsetX, offsetY, rotation }) } // Once this factor's sweep is complete, hide ALL its multiples up to maxN // (covers composites beyond SWEEP_MAX_N visible when viewport zooms out) if (linearProgress >= 1) { for (let m = firstMultiple; m <= maxN; m += p) { if (alreadyMarked.has(m)) continue alreadyMarked.add(m) transforms.set(m, { opacity: 0, offsetX: 0, offsetY: 0, rotation: 0 }) } } } // Safety net: once all sweeps are complete, hide ANY remaining composite // not caught by factors 2,3,5,7,11 (e.g. 169=13²) const lastPhase = SIEVE_PHASES[SIEVE_PHASES.length - 1] const allSweepsComplete = dwellElapsedMs >= lastPhase.startMs + lastPhase.durationMs if (allSweepsComplete) { for (let n = 4; n <= maxN; n++) { if (transforms.has(n)) continue if (smallestPrimeFactor(n) === n) continue // prime — leave alone transforms.set(n, { opacity: 0, offsetX: 0, offsetY: 0, rotation: 0 }) } } // Composition reveal: fade the example composite back in as a ghost if (dwellElapsedMs >= COMPOSITION_START_MS) { const ghostT = clamp01((dwellElapsedMs - COMPOSITION_START_MS - 800) / 600) // delay + fade if (ghostT > 0) { transforms.set(COMPOSITION_EXAMPLE, { opacity: ghostT * 0.5, // semi-transparent ghost offsetX: 0, offsetY: 0, rotation: 0, }) } } return transforms } // --- Main renderer --- /** * Render the animated Sieve of Eratosthenes overlay with "shake out" animation. * Each composite flashes its number, shakes, then falls off the number line. * Called each frame during the "ancient-trick" prime tour stop. */ export function renderSieveOverlay( ctx: CanvasRenderingContext2D, state: NumberLineState, cssWidth: number, cssHeight: number, isDark: boolean, dwellElapsedMs: number, tourOpacity: number ): void { if (tourOpacity <= 0) return ctx.save() ctx.globalAlpha = tourOpacity const centerY = cssHeight / 2 // Visible range in number-line units (used only for visibility culling) const EDGE_BUFFER = 5 const halfRange = cssWidth / (2 * state.pixelsPerUnit) const leftValue = state.center - halfRange const rightValue = state.center + halfRange const visibleMin = Math.max(2, Math.floor(leftValue) - EDGE_BUFFER) const visibleMax = Math.ceil(rightValue) + EDGE_BUFFER // Compute all composite animation states using fixed sweep range // (SWEEP_MAX_N keeps timing in sync with viewport tracking) const composites = computeCompositeStates(SWEEP_MAX_N, dwellElapsedMs, rightValue) // --- Layer 0: Celebration axis wash (dims composites drawn by main renderer) --- if (dwellElapsedMs >= CELEBRATION_START_MS) { const celebrationElapsed = dwellElapsedMs - CELEBRATION_START_MS const washRamp = clamp01(celebrationElapsed / 800) const washAlpha = 0.4 * washRamp ctx.fillStyle = isDark ? `rgba(26, 26, 46, ${washAlpha})` : `rgba(248, 248, 248, ${washAlpha})` ctx.fillRect(0, 0, cssWidth, cssHeight) } // --- Layer 1: Flash glow ring on composites as sweep reaches them --- // The main renderer handles tick+label transforms (shake, fall, hide). // The overlay only draws the glow marking effect during the flash phase. for (const [value, anim] of composites) { if (value < visibleMin || value > visibleMax) continue const localTime = dwellElapsedMs - anim.markTimeMs if (localTime < 0 || localTime > FLASH_DURATION) continue const baseX = numberToScreenX(value, state.center, state.pixelsPerUnit, cssWidth) const t = localTime / FLASH_DURATION const glowRadius = 12 + 8 * easeOutQuint(t) const glowAlpha = 0.5 + 0.3 * (1 - t) const gradient = ctx.createRadialGradient(baseX, centerY, 0, baseX, centerY, glowRadius) gradient.addColorStop(0, primeColorRgba(anim.factor, glowAlpha, isDark)) gradient.addColorStop(1, primeColorRgba(anim.factor, 0, isDark)) ctx.beginPath() ctx.arc(baseX, centerY, glowRadius, 0, Math.PI * 2) ctx.fillStyle = gradient ctx.fill() } // --- Shared arc peak height for path + hopper --- // Both Layer 2a (path arcs) and Layer 2b (hopper) use this so they align exactly. function computeArcPeak(screenDist: number): number { return Math.min(30, Math.max(8, Math.abs(screenDist) * 0.35)) } // --- Layer 2a: Viewport-wide skip arcs (the "hopper path") --- // Repeating arcs across the visible range at the current skip distance. // During transitions between factors the skip distance morphs smoothly. { let skipDist: number | null = null let arcColorFactor = 2 let arcAlpha = 1 // Determine effective skip distance + color for the current time for (let i = 0; i < SIEVE_PHASES.length; i++) { const phase = SIEVE_PHASES[i] const phaseEnd = phase.startMs + phase.durationMs // During a sweep phase if (dwellElapsedMs >= phase.startMs && dwellElapsedMs < phaseEnd) { skipDist = phase.factor arcColorFactor = phase.factor break } // In a gap/tail between phases: morph skip distance const nextPhase = SIEVE_PHASES[i + 1] if (nextPhase && dwellElapsedMs >= phaseEnd && dwellElapsedMs < nextPhase.startMs) { const gapT = clamp01((dwellElapsedMs - phaseEnd) / (nextPhase.startMs - phaseEnd)) const eased = easeOutCubic(gapT) skipDist = lerp(phase.factor, nextPhase.factor, eased) arcColorFactor = gapT < 0.5 ? phase.factor : nextPhase.factor break } } // Before first phase: fade in arcs at factor 2 spacing if (skipDist === null && dwellElapsedMs < SIEVE_PHASES[0].startMs) { skipDist = SIEVE_PHASES[0].factor arcColorFactor = SIEVE_PHASES[0].factor arcAlpha = clamp01(dwellElapsedMs / 1500) // fade in over 1.5s } // After last phase: fade out during celebration if (skipDist === null && dwellElapsedMs >= CELEBRATION_START_MS) { arcAlpha = 0 } // Between last phase end and celebration: hold last factor, start fading const lastP = SIEVE_PHASES[SIEVE_PHASES.length - 1] const lastEnd = lastP.startMs + lastP.durationMs if (skipDist === null && dwellElapsedMs >= lastEnd && dwellElapsedMs < CELEBRATION_START_MS) { skipDist = lastP.factor arcColorFactor = lastP.factor arcAlpha = 1 - clamp01((dwellElapsedMs - lastEnd) / (CELEBRATION_START_MS - lastEnd)) } // Draw the repeating arcs if (skipDist !== null && arcAlpha > 0.01) { // Start from the leftmost visible skip boundary const startN = Math.floor(leftValue / skipDist) * skipDist const endN = rightValue + skipDist for (let n = startN; n < endN; n += skipDist) { const aFromSX = numberToScreenX(n, state.center, state.pixelsPerUnit, cssWidth) const aToSX = numberToScreenX(n + skipDist, state.center, state.pixelsPerUnit, cssWidth) if (aToSX < -50 || aFromSX > cssWidth + 50) continue const arcPeak = computeArcPeak(aToSX - aFromSX) ctx.beginPath() ctx.moveTo(aFromSX, centerY) ctx.quadraticCurveTo((aFromSX + aToSX) / 2, centerY - arcPeak, aToSX, centerY) ctx.strokeStyle = primeColorRgba(arcColorFactor, 0.15 * arcAlpha, isDark) ctx.lineWidth = 1.5 ctx.stroke() } } } // --- Layer 2b: Skip-counting hopper --- // A dot that hops along the path arcs. Traces the exact same quadratic Bezier curve. // The hopper "stomps" new composites (full arc) and "skims" already-gone ones (low arc). { let hopperPhase: SievePhase | null = null for (let i = SIEVE_PHASES.length - 1; i >= 0; i--) { const phase = SIEVE_PHASES[i] if (dwellElapsedMs < phase.startMs) continue const lp = clamp01((dwellElapsedMs - phase.startMs) / phase.durationMs) if (lp >= 1) continue hopperPhase = phase break } if (hopperPhase) { const p = hopperPhase.factor const linearProgress = clamp01( (dwellElapsedMs - hopperPhase.startMs) / hopperPhase.durationMs ) const progress = sweepEase(linearProgress, p) const sweepStart = p const sweepRange = SWEEP_MAX_N - sweepStart const sweepValue = sweepStart + sweepRange * progress // Which two multiples of p are we between? const fromMultiple = Math.max(p, Math.floor(sweepValue / p) * p) const toMultiple = fromMultiple + p const hopT = clamp01((sweepValue - fromMultiple) / p) // Skim vs. stomp: is the landing target already eliminated by an earlier factor? const targetAlreadyGone = toMultiple > p && smallestPrimeFactor(toMultiple) < p const skimScale = targetAlreadyGone ? 0.12 : 1 // Convert to screen space const fromSX = numberToScreenX(fromMultiple, state.center, state.pixelsPerUnit, cssWidth) const toSX = numberToScreenX(toMultiple, state.center, state.pixelsPerUnit, cssWidth) const screenDist = toSX - fromSX // Arc height: match the path arcs' quadratic Bezier exactly. // Quadratic Bezier with control point at (midX, centerY - arcPeak): // y(t) = centerY - arcPeak * 2 * t * (1 - t) // For skims, scale the peak down. const arcPeak = computeArcPeak(screenDist) * skimScale const arcHeight = arcPeak * 2 * hopT * (1 - hopT) // Hopper screen position const hopperSX = fromSX + hopT * screenDist const hopperY = centerY - arcHeight // Ghost label for already-gone composites: brief fade-in/out near landing if (targetAlreadyGone && hopT > 0.4) { const ghostAlpha = Math.sin(Math.PI * clamp01((hopT - 0.4) / 0.6)) * 0.55 if (ghostAlpha > 0.01) { ctx.save() ctx.globalAlpha = ghostAlpha * tourOpacity ctx.font = 'bold 13px system-ui, sans-serif' ctx.textAlign = 'center' ctx.textBaseline = 'top' ctx.fillStyle = isDark ? '#888' : '#999' ctx.fillText(String(toMultiple), toSX, centerY + 5) const textWidth = ctx.measureText(String(toMultiple)).width ctx.beginPath() ctx.moveTo(toSX - textWidth / 2 - 2, centerY + 12) ctx.lineTo(toSX + textWidth / 2 + 2, centerY + 12) ctx.strokeStyle = isDark ? '#888' : '#999' ctx.lineWidth = 1.5 ctx.stroke() ctx.restore() } } // Hopper dot (smaller + translucent for skims) const dotRadius = targetAlreadyGone ? 3.5 : 6 const dotAlpha = targetAlreadyGone ? 0.35 : 0.9 ctx.beginPath() ctx.arc(hopperSX, hopperY, dotRadius, 0, Math.PI * 2) ctx.fillStyle = primeColorRgba(p, dotAlpha, isDark) ctx.fill() // Glow around hopper const glowRadius = dotRadius * 2.5 const glow = ctx.createRadialGradient(hopperSX, hopperY, 0, hopperSX, hopperY, glowRadius) glow.addColorStop(0, primeColorRgba(p, targetAlreadyGone ? 0.2 : 0.35, isDark)) glow.addColorStop(1, primeColorRgba(p, 0, isDark)) ctx.beginPath() ctx.arc(hopperSX, hopperY, glowRadius, 0, Math.PI * 2) ctx.fillStyle = glow ctx.fill() } } // Factor spotlight glow (pulsing highlight on the prime factor being used) for (const phase of SIEVE_PHASES) { if (dwellElapsedMs < phase.startMs) break const phaseProgress = clamp01((dwellElapsedMs - phase.startMs) / phase.durationMs) if (phaseProgress >= 1) continue const factorX = numberToScreenX(phase.factor, state.center, state.pixelsPerUnit, cssWidth) const glowRadius = 20 const pulsePhase = (dwellElapsedMs / 300) % (Math.PI * 2) const pulseAlpha = 0.2 + 0.1 * Math.sin(pulsePhase) const gradient = ctx.createRadialGradient(factorX, centerY, 0, factorX, centerY, glowRadius) gradient.addColorStop(0, primeColorRgba(phase.factor, pulseAlpha, isDark)) gradient.addColorStop(1, primeColorRgba(phase.factor, 0, isDark)) ctx.beginPath() ctx.arc(factorX, centerY, glowRadius, 0, Math.PI * 2) ctx.fillStyle = gradient ctx.fill() } // --- Layer 3: Prime celebration (after all sweeps) --- if (dwellElapsedMs >= CELEBRATION_START_MS) { const celebrationElapsed = dwellElapsedMs - CELEBRATION_START_MS const celebrationRamp = clamp01(celebrationElapsed / 800) for (let n = visibleMin; n <= visibleMax; n++) { if (n < 2) continue if (smallestPrimeFactor(n) !== n) continue // not a prime const sx = numberToScreenX(n, state.center, state.pixelsPerUnit, cssWidth) // Pulsing radial glow const glowRadius = 20 const phaseOffset = n * 0.07 const pulsePhase = dwellElapsedMs / 400 + phaseOffset const pulseAlpha = (0.25 + 0.15 * Math.sin(pulsePhase)) * celebrationRamp const gradient = ctx.createRadialGradient(sx, centerY, 0, sx, centerY, glowRadius) gradient.addColorStop(0, primeColorRgba(n, pulseAlpha, isDark)) gradient.addColorStop(1, primeColorRgba(n, 0, isDark)) ctx.beginPath() ctx.arc(sx, centerY, glowRadius, 0, Math.PI * 2) ctx.fillStyle = gradient ctx.fill() // Prime labels are drawn by the main renderer — no overlay labels needed } } // --- Layer 4: Composition reveal (after celebration) --- // Shows skip-counting paths that reach the example composite, revealing its factorization. if (dwellElapsedMs >= COMPOSITION_START_MS) { const compElapsed = dwellElapsedMs - COMPOSITION_START_MS const chains = compositionChains(COMPOSITION_EXAMPLE) const factors = primeFactors(COMPOSITION_EXAMPLE) // Viewport zoom-in transition (fade out celebration glow, fade in composition) const compRamp = clamp01(compElapsed / 1000) // Dim the celebration glows so composition arcs stand out if (compRamp > 0) { const dimAlpha = 0.3 * compRamp ctx.fillStyle = isDark ? `rgba(26, 26, 46, ${dimAlpha})` : `rgba(248, 248, 248, ${dimAlpha})` ctx.fillRect(0, 0, cssWidth, cssHeight) } // Draw skip-counting arc chains, staggered by factor let arcTimeOffset = 500 // initial delay for viewport to settle for (const chain of chains) { const { factor, multiples } = chain // Each arc in the chain appears sequentially for (let i = 0; i < multiples.length - 1; i++) { const arcStartMs = arcTimeOffset + i * COMPOSITION_ARC_STAGGER_MS const arcT = clamp01((compElapsed - arcStartMs) / 400) // 400ms to draw each arc if (arcT <= 0) continue const fromN = multiples[i] const toN = multiples[i + 1] const fromSX = numberToScreenX(fromN, state.center, state.pixelsPerUnit, cssWidth) const toSX = numberToScreenX(toN, state.center, state.pixelsPerUnit, cssWidth) // Same arc shape as the hopper path const arcPeak = computeArcPeak(toSX - fromSX) // Draw the arc with growing alpha const alpha = easeOutCubic(arcT) * 0.6 ctx.beginPath() ctx.moveTo(fromSX, centerY) ctx.quadraticCurveTo((fromSX + toSX) / 2, centerY - arcPeak, toSX, centerY) ctx.strokeStyle = primeColorRgba(factor, alpha, isDark) ctx.lineWidth = 2.5 ctx.stroke() // Small dot at each landing point if (arcT > 0.5) { const dotAlpha = clamp01((arcT - 0.5) * 2) * 0.7 ctx.beginPath() ctx.arc(toSX, centerY, 3, 0, Math.PI * 2) ctx.fillStyle = primeColorRgba(factor, dotAlpha, isDark) ctx.fill() } } // Offset the next factor's chain so they appear sequentially arcTimeOffset += multiples.length * COMPOSITION_ARC_STAGGER_MS + 400 } // Factorization label: "2 × 2 × 3 = 12" const labelDelayMs = arcTimeOffset + 200 const labelT = clamp01((compElapsed - labelDelayMs) / 600) if (labelT > 0) { const exampleSX = numberToScreenX( COMPOSITION_EXAMPLE, state.center, state.pixelsPerUnit, cssWidth ) const labelAlpha = easeOutCubic(labelT) // Build label like "2 × 2 × 3 = 12" const labelStr = factors.join(' × ') + ' = ' + COMPOSITION_EXAMPLE ctx.save() ctx.globalAlpha = labelAlpha * tourOpacity ctx.font = 'bold 16px system-ui, sans-serif' ctx.textAlign = 'center' ctx.textBaseline = 'bottom' ctx.fillStyle = isDark ? '#e0e0e0' : '#333' // Background pill for readability const textWidth = ctx.measureText(labelStr).width const pillPadX = 8 const pillPadY = 4 const pillY = centerY - 45 ctx.fillStyle = isDark ? 'rgba(26, 26, 46, 0.85)' : 'rgba(255, 255, 255, 0.85)' const pillLeft = exampleSX - textWidth / 2 - pillPadX const pillRight = exampleSX + textWidth / 2 + pillPadX const pillTop = pillY - 16 - pillPadY const pillBot = pillY + pillPadY const pillRadius = 6 ctx.beginPath() ctx.moveTo(pillLeft + pillRadius, pillTop) ctx.lineTo(pillRight - pillRadius, pillTop) ctx.quadraticCurveTo(pillRight, pillTop, pillRight, pillTop + pillRadius) ctx.lineTo(pillRight, pillBot - pillRadius) ctx.quadraticCurveTo(pillRight, pillBot, pillRight - pillRadius, pillBot) ctx.lineTo(pillLeft + pillRadius, pillBot) ctx.quadraticCurveTo(pillLeft, pillBot, pillLeft, pillBot - pillRadius) ctx.lineTo(pillLeft, pillTop + pillRadius) ctx.quadraticCurveTo(pillLeft, pillTop, pillLeft + pillRadius, pillTop) ctx.closePath() ctx.fill() // Draw each factor in its prime color, operators in neutral ctx.textBaseline = 'bottom' let curX = exampleSX - textWidth / 2 for (let i = 0; i < factors.length; i++) { const fStr = String(factors[i]) ctx.fillStyle = primeColorRgba(factors[i], 1, isDark) ctx.fillText(fStr, curX + ctx.measureText(fStr).width / 2, pillY) curX += ctx.measureText(fStr).width if (i < factors.length - 1) { ctx.fillStyle = isDark ? '#aaa' : '#666' ctx.fillText(' × ', curX + ctx.measureText(' × ').width / 2, pillY) curX += ctx.measureText(' × ').width } } // " = 12" const eqStr = ' = ' + COMPOSITION_EXAMPLE ctx.fillStyle = isDark ? '#e0e0e0' : '#333' ctx.fillText(eqStr, curX + ctx.measureText(eqStr).width / 2, pillY) ctx.restore() } } ctx.restore() } |